Multiple integrals

W L Bragg [7] observed that if a crystal was composed of copies of identical unit cells, it could then be divided in many ways into slabs with parallel, plane faces whose distributions of scattering matter were identical and that if the pathlengths travelled by waves reflected from successive, parallel planes differed by integral multiples of the... 

Rather than calculate the etithaltty conti ibutioti of the torsional states individually, an empirical sum that is an integral multiple of 0.42 kcal mol per torsional degree of freedom is assigned to flexible molecules in MM3, Torsional motion of a methyl gntup is iK)t added k) a calculated because it is included in the... 

One substitutes integral numbers (guesses) for z (oxygen) and y (nitrogen) until the divisor becomes an integral multiple of the numerator within 0.0002 mass unit. 

Frequency-Modulation Spectroscopy. Frequency-modulation spectroscopy (tins) is a high sensitivity null-background infrared technique for measuring absorbances down to 10 with fast acquisition speeds. Fms involves frequency-modulating a laser source at COq to produce a carrier frequency having sidebands at cJq where is an integral multiple of the modulation frequency. Dye lasers and many other single-line sources can... 

Low molecular weight olefins ranging from to Q, are produced by the polymerization of propylene or butylenes over a supported phosphorie acid catalyst. The product of this polymerization is a series of highly branched olefins ranging from dimers to pentamers. Some fragmentation of the polymers formed takes place in the reactor, so appreciable quantities of olefins are obtained which are not integral multiples of the monomer units. 

A little earlier, in 1815, the London based physician, William Prout, proposed another general principle. In a few papers, which he published anonymously, Prout wrote that the fact that the atomic weights of many elements seemed to be integral multiples of the weight of hydrogen suggested that all... 

TRPVl, also known as the capsaicin- or vanilloid-receptor, is a nonselective cation channel expressed e.g., in neurons of the dorsal root and trigeminal ganglions, which integrates multiple pain-producing stimuli including heat, protons, capsaicin, and resiniferatoxin. In addition, TRPVl currents can be activated by ananda-mide, protein kinase C (PKC), and by hydrolysis of phosphatidylinositol 4,5-bisphosphate (PIP2). 

In this section, multimedia tools refer to computer-based systems that integrate multiple symbol systems (Salomon, 1979), such as text, audio, video, graph, and animation, to demonstrate chemical entities and/or processes at the macro, submicro, or symbolic levels. In the following, we review four multimedia tools—4M Chem, ChemSense, Molecular Workbench, and Connected Chemistry—and use the design principles suggested by Wu and Shah (2004) to summarize how these tools support students in learning chemistry. 

Consequently, radiation energy is always an integral multiple of the energy of a photon. The energy is given as... 

The molecular formula of the condensation polymer is not an integral multiple of the formula of the monomer molecule owing to the elimination of a by-product, which in this case is water. The most important class of addition polymers consists of those derived from unsaturated monomers, such as the vinyl compounds... 

The constant h and the hypothesis that energy is quantized in integral multiples of hv had previously been introduced by M. Planck (1900) in his study of blackbody radiation. In terms of the angular frequency a> deflned in equation (1.2), the energy E of a photon is... 

Studies conducted in the laboratory provide fundamental data on processes by which a pesticide is degraded and on its mobility. In combination with field observations, which integrate multiple processes, these data describe a pesticide s environmental fate. This section provides a discussion of several important specific analytical issues which should be considered in the design of environmental fate studies to ensure that the data generated address the needs of scientists and regulatory agencies for information on the environmental fate and environmental and ecological impacts of a pesticide to the fullest extent. 

Where appropriate, tables of smoothed, recommended values are given at integral multiples of 10 K over the experimental range of temperatures. Values at 293.15 K and 298.15 K are included when they are in the range of the original data set. The recommended values also have assigned uncertainties. 

If you need to repeatedly regenerate your PDF file, as is often the case in clinical trial reporting, it is easier to integrate PostScript files into a single PDF file with an automated scripted process such as the one listed above. Integrating multiple PDF files into a single PDF file is possible, but it is a manual process within Adobe Acrobat. 

If the reaction in the cell proceeds to unit extent, then the charge nF corresponding to integral multiples of the Faraday constant is transported through the cell from the left to the right in its graphical representation. Factor n follows from the stoichiometry of the cell reaction (for example n = 2 for reaction c or d). The product nFE is the work expended when the cell reaction proceeds to a unit extent and at thermodynamic equilibrium and is equal to the affinity of this reaction. Thus,... 

Normality is some integral multiple of molarity, since there are always some integral number of equivalents per mole. 

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